Simulation of higher harmonics generation in tapping-mode atomic force microscopy

Cataloged from PDF version of article.In tapping-mode atomic force microscopy, nonlinear tip–sample interactions give rise to higher harmonics of the cantilever vibration. We present an electrical circuit to model the atomic force microscope cantilever with its first three flexural eigenmodes. An electrical circuit simulator is used to simulate the tapping-mode operation. Amplitude and phase responses of the third flexural eigenmode are obtained for different sample properties. It is found that amplitude and phase of higher harmonics depend highly on sample properties. © 2001 American Institute of Physic

An Optimized Isolation Network for the Wilkinson Divider

Cataloged from PDF version of article.We propose an isolation network to simultaneously improve the input return loss, output return loss and isolation of the Wilkinson power divider in a wide bandwidth. The required even mode and odd mode reflection coefficients of the isolation network are calculated. Constructed even and odd mode circuits are combined to give the desired isolation network. Analytical expressions for the optimal component values for a single-section divider are given. Compared with the single-section Wilkinson divider, the final design can triple the bandwidth for an input-output return loss and isolation of greater than 25 dB. Broadband characteristic is achieved without increasing the number of sections hence extra length and insertion loss are avoided. Wide operation bandwidth of the new divider is verified by experimental results. The proposed method can be applied to a two-section divider, also broadening its bandwidth

Enhancing higher harmonics of a tapping cantilever by excitation at a submultiple of its resonance frequency

Cataloged from PDF version of article.In a tapping-mode atomic force microscope, the frequency spectrum of the oscillating cantilever contains higher harmonics at integer multiples of the excitation frequency. When the cantilever oscillates at its fundamental resonance frequency w(1), the high Q-factor damps the amplitudes of the higher harmonics to negligible levels, unless the higher flexural eigenmodes are coincident with those harmonics. One can enhance the nth harmonic by the Q factor when the cantilever is excited at a submultiple of its resonance frequency (w(1)/n). Hence, the magnitude of the nth harmonic can be measured easily and it can be utilized to examine the material properties. We show theoretically that the amplitude of enhanced higher harmonic increases monotonically for a range of sample stiffness, if the interaction is dominated by elastic force

Analysis of tip-sample interaction in tapping-mode atomic force microscope using an electrical circuit simulator

Cataloged from PDF version of article.We present a mechanical model for the atomic force microscope tip tapping on a sample. The model treats the tip as a forced oscillator and the sample as an elasticmaterial with adhesiveproperties. It is possible to transform the model into an electrical circuit, which offers a way of simulating the problem with an electrical circuit simulator. Also, the model predicts the energy dissipation during the tip–sample interaction. We briefly discuss the model and give some simulation results to promote an understanding of energy dissipation in a tapping mode. © 2001 American Institute of Physic

Using phase relations in microstrip directional couplers to achieve high directivity

Cataloged from PDF version of article.We analyze the microstrip directional couplers with a special focus on the phase difference between the coupled and isolated ports. The analysis uses the even-odd mode decomposition technique and network theory. The results show that the phase difference between the signals at the coupled port and the isolated port is close to in a very wide band. This property can be used to achieve a broadband directivity by inducing a voltage cancellation at the isolated port of the couplers. Two different cancellation methods are investigated. Analytical formulas for the required component values of both methods are given. Higher directivity can be obtained at the expense of reduced bandwidth

Power dissipation analysis in tapping mode atomic force microscopy

Cataloged from PDF version of article.In a tapping-mode atomic force microscope, a power is dissipated in the sample during the imaging process. While the vibrating tip taps on the sample surface, some part of its energy is coupled to the sample. Too much dissipated power may mean the damage of the sample or the tip. The amount of power dissipation is related to the mechanical properties of a sample such as viscosity and elasticity. In this paper, we first formulate the steady-state tip-sample interaction force by a simple analytical expression, and then we derive the expressions for average and maximum power dissipated in the sample by means of sample parameters. Furthermore, for a given sample elastic properties we can determine approximately the sample damping constant by measuring the average power dissipation. Simulation results are in close agreement with our analytical approach

Binary Sequences With Low Aperiodic Autocorrelation for Synchronization Purposes

Cataloged from PDF version of article.An evolutionary algorithm is used to find three sets of binary sequences of length 49–100 suitable for the synchronization of digital communication systems. Optimization of the sets are done by taking into consideration the type of preamble used in data frames and the phase-lock mechanism of the communication system. The preamble is assumed to be either a pseudonoise (PN) sequence or a sequence of 1’s. There may or may not be phase ambiguity in detection. With this categorization, the first set of binary sequences is optimized with respect to aperiodic autocorrelation which corresponds to the random (PN) preamble without phase ambiguity case. The second and third sets are optimized with respect to a modified aperiodic autocorrelation for different figures of merit corresponding to the predetermined preamble (sequence of 1’s) with and without phase ambiguity cases

Noise analysis of geometrically complex mechanical structures using the analogy between electrical circuits and mechanical systems

Cataloged from PDF version of article.Random fluctuations of displacement or velocity in mechanical systems can be calculated by using the analogy between electrical circuits and mechanical systems. The fluctuation-dissipation theorem expresses the relation between the generalized mechanical admittance and the noise in velocity. Similarly, correlation of mechanical noise can be calculated by using the generalized Nyquist theorem which states that the current noise correlation between two ports in an electrical circuit is dictated by the real part of the transadmittance. In this article, we will present the determination of the mechanical transadmittance and we will use the mechanical transadmittance to calculate the noise correlation on geometrically complex structures where it is not possible to approximate the noise by using the simple harmonic oscillator model. We will apply our method to atomic force microscope cantilevers by means of finite element method tools. The application of the noise correlation calculation method to rectangular cantilever beams shows some interesting results. We found that on the resonance frequencies, the correlation coefficient takes values 1 (full correlation) and -1 (anti-correlation) along the cantilever axis depending on the mode shapes of the structure. (C) 1999 American Institute of Physic

Acoustic Microscopy Via Scanning

We offer via posters some of the latest images recorded with the scanning acoustic microscope operating near 2.5 GHz. Our report at the 1978 Review included a description of the scanning instrument which had been scaled up in frequency to 3 GHz. This was accomplished in large part by fabricating acoustic lens with smaller radii and by heating the liquid to reduce the absorption. In our report for this year, we·will present the results of our material studies as carried out with the new instruments operating near 2.5 GHz. We will include results on four different materials - steel, Cobalt-Titanium, brass and alumina ceramic. Each of these have distinctive characteristics in the acoustic micrographs and each of these have information which is distinct from their optical counterparts

Application of asymptotic waveform evaluation for time domain analysis of nonlinear circuits

Cataloged from PDF version of article.A method is described to exploit asymptotic waveform evaluation (ATNE) in the time-domain analysis of nonlinear circuits by using SPICE models for nonlinear devices such as diodes, transistors, etc. Although AWE has been used for linearized circuits only, the aim is to enhance the accuracy of the simulation while preserving the computational efficiency obtained with AWE and to eliminate the piecewise-linear modelling problem. Practical examples are given to illustrate significant improvements in accuracy. For circuits containing weakly nonlinear devices, it is demonstrated that this method is typically at least one order of magnitude faster than SPICE